If 90% of A = 30% of B and B = 2x% of A, then the value of x is

Options

A. 450
B. 400
C. 300
D. 150

Answer

To solve the problem, we start with the given equations:

1. \( 90\% \text{ of } A = 30\% \text{ of } B \)
2. \( B = 2x\% \text{ of } A \)

### Step 1: Convert percentages to equations
From the first equation, we can express it mathematically:
\[ 0.9A = 0.3B \]

### Step 2: Rearrange the first equation to express B in terms of A
To isolate \( B \), we can rearrange the equation:
\[ B = \frac{0.9A}{0.3} \]
\[ B = 3A \]

### Step 3: Substitute B into the second equation
Now that we have \( B \) in terms of \( A \), we can substitute this into the second equation:
\[ 3A = 2x\% \text{ of } A \]
This can be rewritten as:
\[ 3A = \frac{2x}{100}A \]

### Step 4: Cancel A from both sides
Assuming \( A \neq 0 \), we can divide both sides by \( A \):
\[ 3 = \frac{2x}{100} \]

### Step 5: Solve for x
Now, we can solve for \( x \) by multiplying both sides by 100:
\[ 300 = 2x \]
Now divide both sides by 2:
\[ x = 150 \]

### Final Answer
The value of \( x \) is \( 150 \).

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